Defining parameters
| Level: | \( N \) | \(=\) | \( 4000 = 2^{5} \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4000.bo (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(600\) | ||
| Trace bound: | \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(4000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 360 | 24 | 336 |
| Cusp forms | 40 | 24 | 16 |
| Eisenstein series | 320 | 0 | 320 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 24 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(4000, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 4000.1.bo.a | $8$ | $1.996$ | \(\Q(\zeta_{20})\) | $D_{20}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots\) |
| 4000.1.bo.b | $8$ | $1.996$ | \(\Q(\zeta_{20})\) | $D_{20}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots\) |
| 4000.1.bo.c | $8$ | $1.996$ | \(\Q(\zeta_{20})\) | $D_{20}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(4000, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(4000, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)